reserve e,u for set;
reserve X, Y for non empty TopSpace;

theorem Th36:
  for XX being non empty TopSpace , X being non empty SubSpace of
  XX for D being non empty a_partition of the carrier of X for e being Point of
  XX st Proj TrivExt D.e in the carrier of space D holds e in the carrier of X
proof
  let XX be non empty TopSpace , X be non empty SubSpace of XX;
  let D be non empty a_partition of the carrier of X;
  let e be Point of XX;
  assume Proj TrivExt D.e in the carrier of space D;
  then
A1: Proj TrivExt D.e in D by Def7;
  e in Proj TrivExt D.e by EQREL_1:def 9;
  hence thesis by A1;
end;
